Final answer:
The lines represented by the equations y = -4/5x + 2 and y = 5/4x - 7 are perpendicular to each other because the product of their slopes is -1.
Step-by-step explanation:
To determine if the two lines are parallel, perpendicular, or neither, we need to compare their slopes. The slope of a line is the coefficient of x in the linear equation y = mx + b, where m is the slope. Line 1, given by y = -4/5x + 2, has a slope of -4/5. Line 2, given by y = 5/4x - 7, has a slope of 5/4. If two lines are parallel, they have the same slope. If they are perpendicular, the product of their slopes is -1 because perpendicular slopes are negative reciprocals of each other.
Examining the slopes of Line 1 and Line 2 shows that they are not the same and the product of -4/5 and 5/4 is -1. Therefore, Line 1 and Line 2 are perpendicular to each other.